" /> Applying the Central Limit Theorem to a Real-World Setting - Essay Writing Pros

Applying the Central Limit Theorem to a Real-World Setting

We do not actually know the population proportion unless we conduct an expensive poll of all individuals in the population. Our earlier value of p = 0.88 was based on a Pew Research conducted a poll of 1000 American adults that found p̂ = 0.887 of them favored expanding solar energy. The researchers might have wondered: does the sample proportion from the poll approximately follow a normal distribution? We can check the conditions from the Central Limit Theorem:

Independence. The poll is a simple random sample of American adults, which means that the observations are independent.

Don't use plagiarized sources. Get Your Custom Essay on
Applying the Central Limit Theorem to a Real-World Setting
Just from \$13/Page

Success-failure condition. To check this condition, we need the population proportion, p, to check if both np and n(1− p) are greater than 10. However, we do not actually know p, which is exactly why the pollsters would take a sample! In cases like these, we often use p̂ as our next best way to check the success-failure condition:

np̂ = 1000× 0.887 = 887 n(1− p̂) = 1000× (1− 0.887) = 113

The sample proportion p̂ acts as a reasonable substitute for p during this check, and each value in this case is well above the minimum of 10.

This substitution approximation of using p̂ in place of p is also useful when computing the standard error of the sample proportion:

SEp̂ =

√ p(1− p)

n ≈ √ p̂(1− p̂)

n =

√ 0.887(1− 0.887)

1000 = 0.010

This substitution technique is sometimes referred to as the “plug-in principle”. In this case, SEp̂ didn’t change enough to be detected using only 3 decimal places versus when we completed the calculation with 0.88 earlier. The computed standard error tends to be reasonably stable even when observing slightly different proportions in one sample or another.

5Since the sample size n is in the denominator (on the bottom) of the fraction, a bigger sample size means the entire expression when calculated will tend to be smaller. That is, a larger sample size would correspond to a smaller standard error.

Pages (550 words)
Approximate price: -

Why Work with Us

Top Quality and Well-Researched Papers

Our writers have been trained on how to handle papers placed by our clients. The writer must read and understand before embarking on writing the papers. In case of any issue that needs clarification, writers are encouraged to ask the client or support.

Our team comprises of the best writers and editors. We do thorough vetting during recruitment to make sure that our writers have the knowledge and experience we aspire in the team.

Free Unlimited Revisions

Our aim is to give the client the best outcome. If for some reason you are not satisfied with the wok done, you can ask the paper to be revised or rewritten. This will be done to your satisfaction with no extra charges.

Prompt Delivery and 100% Money-Back-Guarantee

We have writers who work round the clock. This helps in making sure that all our clients’ papers are delivered on time. If we have issues with the deadline, we will ask for extension. If its not possible, the money is fully refunded.

Original & Confidential

Our clients’ confidentiality is highly respected. We can never disclose our clients’ details to third parties. In the same regard, we strive to give our clients 100% original papers. We do not tolerate plagiarism from our writers.

Clients can reach us any time of the day, and any day of the week. There is a live chat, email or phone numbers to help in ease of communication.

Try it now!

Calculate the price of your order

Total price:
\$0.00

How it works?

Fill in the order form and provide all details of your assignment.

Proceed with the payment

Choose the payment system that suits you most.

Our Services

You should never be worried about your papers even in the middle of the night. Our team will work round the clock to deliver.

Essay Writing Service

We have an able team that can deliver your work in the shortest time possible. The academic level or the type of work should never be a hindrance. Our highly competent support team is always around (24/7) to give you any assistance you may need.